1×N and N×N fiber optic couplers

ABSTRACT

The present invention provides fiber optic couplers for use with at least three optic fibers. The optic fibers arranged in a linear array, that is, the optic fibers are coupled side by side. The fibers along either end of the linear-array are coupled only to a single fiber, while the remaining fibers are generally coupled between only two adjacent fibers. Generally, at least one of the fibers has a propagation constant different than the other fibers. Such variations in the propagation constant are used to vary the coupling coefficients among the fibers of the linear-array, thereby providing a repeatable mechanism, to vary coupled power ratios among the fibers of the coupler. Theoretical calculations and empirical experience have shown that varying the propagation constant of fibers among a linear-array, generally by pre-pulling the fibers by varying amounts, allows repeatable manufacturing of 1×3, 3×3, 1×4, 4×4, 1×N and even N×N fiber couplers having even coupled power ratios.

BACKGROUND OF THE INVENTION

The present invention is related to fiber optic technology, and moreparticularly, to fiber optic couplers for single mode optic fibers.

Modern fiber optic networks generally use single mode optic fibers totransmit light signals having a particular wavelength. Such networkstypically have numerous couplers by which a signal on one fiber isdistributed to two or more fibers. In a typical coupler, a single inputfiber joins two output fibers to form a 1×2 coupler, or two input fibersjoin two output fibers to form a 2×2 coupler. Previously, a number ofthese simple couplers were connected together in series to providecoupling between larger numbers of input and output fibers. Morerecently, monolithic 1×N and N×N couplers have been proposed to couplelarger numbers of fibers.

A wide variety of monolithic coupler geometries have been proposed.These known monolithic optic couplers have generally been formed astight bundles, in which each optical fiber is coupled to severalsurrounding optical fibers, or on occasion, to a central optical elementin an axisymmetric arrangement. The interaction within these coupledstructures can be quite complex, in part because the fused opticalelements may form a waveguide which supports several propagation modes.Further complicating any analysis of these monolithic 1×N and N×Ncouplers is the real world existence of non-uniformity in the opticalfiber bundle. The complex results of unequal fiber fusing in a simpletriangular optic fiber bundle were analyzed by B. Michael Kale in"Performance of Lightly-Fused, Sharply-Tapered 3×3 Single Mode FiberOptic Couplers," SPIE PROC., Vol. 839, Components For Fiber OpticApplications II, 1987, pp. 48-57. Where larger numbers of fibers arebundled together, analysis of these dimensional errors gets morecomplex, and the resulting non-uniformity in coupled power ratios maybecome more difficult to calculate and to avoid. Geometric distortionand the resulting inaccuracy in coupled power ratios appears to bedifficult to eliminate within known bundled fiber geometries,particularly when the bundles of optical fibers are tightly bound withincapillary tubes prior to tapering. Nonetheless, a wide variety of suchbundled and clad monolithic fiber couplers have been proposed.

Another problem with many known optic couplers is that the coupled powerratios provided at the output ends to be wavelength dependent. Althoughthe semiconductor lasers used to generate signals for modern opticnetworks are nominally coherent, the actual light signals produced aretypically no more precise than ±30 nanometers of the nominal wavelength.To properly distribute these fairly noisy semiconductor laser generatedsignals, it is generally desirable that couplers distribute the signalsproperly regardless of the actual signal wavelength. In other words, itis generally preferable to provide couplers which are insensitive towavelength variations. This helps to ensure that the strength of thesignal on an arbitrary branch of a fiber optic network will be coupledproperly.

While known 1×N and N×N optical couplers have been found to haveadvantages over couplers built up with several 1×2 or 2×2 devices, it isdesirable to provide monolithic optic fiber couplers having improvedwavelength response for high performance fiber optic networks.Furthermore, the described coupler fabrication techniques have proved todifficult to implement, and predictably and reliably reproducing desiredcoupled power ratios has proven to be particularly problematic. Withoutpredictability, reproducibility, and manufacturability, the cost forthese couplers has remained high, and implementation of fiber opticnetworks has thereby been inhibited.

SUMMARY OF THE INVENTION

The present invention provides monolithic 1×N and N×N fiber opticcouplers having a linear-array geometry, that is, the optic fibers arecoupled side-by-side in a single row. The fibers along either edge ofthe linear-array are coupled only to a single inner fiber along at leasta position of the linear array, while the inner fibers are coupledbetween two adjacent fibers. Generally, at least one of the fibers has apropagation constant different than an adjacent fiber. Such variationsin the propagation constants among the fibers of a linear-array providea controllable, repeatable mechanism to vary the coupling coefficientsof the individual fused joints between adjacent fibers. Theoreticalcalculations and empirical experience have shown that a linear-arraygeometry of dissimilar optic fibers in a twist-parallel-twist couplerarrangement will allow repeatable manufacturing of 1×4, 4×4, 1×N, andeven N×N fiber couplers having even coupled power ratios. Alternatively,through a combination of the linear-array geometry, thetwist-parallel-twist coupler arrangement, and controlled pre-pulling ofselected fibers, optic couplers having any of a variety of alternativedesirable power split characteristics can be produced.

In a first aspect, the present invention provides a fiber optic couplercomprising at least four optic fibers. The optic fibers are coupledtogether along a coupled length, and have input and output endsextending from that coupled length. At least two of the optic fiberscomprises inner fibers which are coupled between two adjacent opticfibers. Two of the optic fibers comprise edge fibers which are eachcoupled directly only to one of the other fibers along the coupledlength. A propagation constant of a first of the optic fibers isdifferent than propagation constants of a second optic fiber along thecoupled length, and output light signals of substantially equal powerare produced at the output ends of the fibers when a light signal isintroduced at the input end of one of the fibers.

In another aspect, the present invention provides a fiber optic couplercomprising a plurality of optic fibers, each optic fiber defining anaxis. The optic fibers are coupled along a coupled length, and apropagation constant of a first of the optic fibers is different thanpropagation constants of second and third fibers along the coupledlength. A first twist is defined by a first axial portion of two of theoptic fibers, each of the twisted optic fibers at the first twist havinga pitch. A second twist is similarly defined by a second axial portionof the twisted optic fibers, each of the twisted optic fibers at thesecond twist also having a pitch. A substantially parallel portion isdisposed between the first twist and the second twist. The pitch of theparallel portion is less than the pitch of the twisted optic fibers atthe first and second twists, and the coupled length extends along atleast a portion of the parallel portion. The optic fibers are coupledside-by-side in a single row to define a linear-array along the parallelportion, and the twisted optic fibers are disposed along opposed edgesof the linear-array.

Generally, the ratios of coupling coefficients between adjacent axialfibers varies across the linear array. This variation in couplingcoefficient ratios, which can be achieved by simple pre-pulling ofalternating optic fibers, allows predetermined arbitrary power couplingratios to be achieved by varying the coupled length and monitoring thecoupler's performance.

In another aspect, the present invention provides a fiber optic couplercomprising at least three optic fibers. Each fiber has a core and asurrounding cladding, an input end, and an output end. The fibers arecoupled along a coupled length between the input and output ends, and apropagation constant of a first of the fibers is different than that ofan adjacent second optic fiber. Coupled power ratios between one of theinput ends and the output ends of at least two of the optic fibers aresubstantially equal over a range of light signal frequencies. However, acoupled power ratio between one of the output ends and the input end islower than the equal power ratios. Surprisingly, the presence of thislow-power fiber enhances the frequency range of light signals thatprovide the equal power ratios.

In another aspect, the present invention provides a method forfabricating optic fiber couplers. At least three optic fibers areprovided, at least one of the optic fibers having a propagation constantwhich is different than another of the optic fibers. The fibers arearranged side-by-side in a single row so that two edge fibers aredisposed along opposed edges of the row. The fibers are fused togetherinto a linear-array along a coupled length. The fibers are heated andpulled axially to increase the coupled length. The heating and pullingsteps are stopped when the optic fibers exhibit predetermined coupledpower ratios. Advantageously, the predetermined coupled power ratios ofthe stopping step may comprise any of a plurality of alternative targetcoupling characteristics described hereinbelow.

In another aspect, the present invention provides a method forfabricating optic fiber couplers. The method comprises providing atleast three optical fibers, one having a propagation constant which isdifferent than a propagation constant of another. The fibers are fusedalong a coupled length between input ends and output ends of each of thefibers, and are heated along the coupled length and pulled axially toincrease the coupled length. The heating and pulling steps are stoppedwhen the fibers exhibit any of a plurality of alternative predeterminedcoupling characteristics between any of the input ends and the outputends.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1A-1J illustrate known bundled or axisymmetric fiber opticcouplers having three or more optic fibers.

FIGS. 2 and 2A illustrate a fiber optic coupler having four optic fibersarranged in a linear array, in which alternating fibers have beenpre-pulled to vary their propagation constants and the couplingcoefficients of the fused joints between the fibers, according to theprinciples of the present invention.

FIGS. 3 and 3A illustrate an optical coupler having three optic fibersarranged in a linear array, in which the center fiber has beenpre-pulled to vary its propagation constant.

FIG. 4 illustrates a cross-section of a linear array fiber opticcoupler, and illustrates that geometric distortions have a limitedeffect on the fused joints between the fibers of the array.

FIG. 5 illustrates a simplified cross-section of a fiber optic couplerhaving three uniform fibers, as used to model the theoreticalperformance of such structures hereinbelow.

FIGS. 5A and B illustrate the variations in light intensity versuscoupler length for a linear array fiber optic coupler having threeuniform fibers with uniform coupling constants.

FIG. 6 illustrates a simplified cross-section of an fiber optic couplerhaving four fibers, as used to model the theoretical performance of suchstructures hereinbelow.

FIGS. 6A-C illustrate the variations in light intensity versus couplerlength for a linear array fiber optic coupler having four uniform fiberswith uniform coupling constants therebetween.

FIGS. 7A and B illustrate the wavelength and insertion losscharacteristics of couplers having four uniform optic fibers in thebundled configuration of FIG. 1B, and in the linear-array configurationof FIGS. 2 and 2A, respectively.

FIG. 8 illustrates the variations in light intensity versus couplerlength for a linear-array 1×4 fiber optic coupler having fibers whichhave been selectively pre-pulled to vary the coupling constants of thefused joints between fibers.

FIGS. 9A and 9B illustrate the improvement in bandwidth provided bypre-pulling selected fibers of a linear-array.

FIGS. 10A-10D illustrate optic coupler power ratios for linear arrayoptic fiber couplers having three fibers, in which the variation inpower ratio versus wavelength provide a variety of specific targetcharacteristics which are advantageous for use in optic fiber networks.

FIG. 11 illustrates a method of making the fiber optic coupler of FIG.2.

FIG. 12 illustrates a clip which holds the optic fibers in a single row,for use in the method of FIG. 11.

DETAILED DESCRIPTION OF THE SPECIFIC EMBODIMENTS

The present invention provides linear-array fiber optic couplers andmethods for their production. The side-by-side coupling of the opticfibers within these linear-arrays, in combination with controlledvariation in the ratios of coupling coefficients between adjacentfibers, allows predicable and repeatable manufacturing processes to beemployed which can produce a wide variety of advantageouspower-splitting characteristics. Variations in coupling coefficientratios are typically provided by pre-pulling selected optical fibers soas to vary their propagation constants.

Referring now to FIGS. 1A-1J, a wide variety of monolithic couplercross-sectional geometries have previously been proposed. Typically,optic fiber couplers are formed by fusing a plurality of optic fibers10. These optic fibers, in turn, are each formed from a central core 12surrounded by a cladding 14. In modern optic fiber networks, core 12 istypically as small as 2 to 10 micrometers, so that each independentfiber will support only a single mode of light propagation. However, byfusing a multiple discreet optic fibers together, light is able topropagate from a core, through the cladding of the two fibers, and intothe adjacent core. Unfortunately, as more and more optical fibers arebundled together, light propagating along the wave guide provided by thecombined optic fibers can propagate in a rapidly increasing number ofmodes.

Additionally, evenly and predictably fusing just three optic fibers in atriangular arrangement, as illustrated in FIG. 1A, can be problematic.As described by B. Michael Kale in an article entitled "Performance ofLightly-Fused, Sharply-Tapered 3×3 Single-Mode Fiber Optic Couplers,"Components For Fiber Optic Applications II, SPIE, Vol. 839 (1987),triangular fused couplers often end up quite distorted during themanufacturing process, so that the fused connections between fibers areuneven. Such uneven fusing is especially problematic in couplers havinglarger numbers of fibers, such as those shown in FIGS. 1C and 1D.Alternative fiber based couplers have included capillary tubes 16surrounding the fibers, or central wave guides 18, such as the fluorinedoped rod illustrated in the known coupler embodiment shown in FIGS. 1Iand 1J.

Although individual optic fiber couplers have been successfully producedin several of the configurations illustrated in FIGS. 1A-1J, includingindividual couplers having fairly even power-splitting characteristics,these known optic fiber couplers generally suffer from high loss, unevenpower sharing, high manufacturing costs, high rejection rates, and/ordifficulty in correlating the anticipated and actual couplingperformance.

Referring now to FIG. 2, a linear-array fiber optic coupler 20 comprisesfour optic fibers 10A-10D. These fibers are arranged side-by-side alonga substantial portion of the length of the coupler, in which fiber 10Ais directly adjacent only to fiber 10B, while fiber 10D is directlyadjacent only to fiber 10C. Fibers 10B and 10C are each disposed betweentwo adjacent fibers, as can be seen in the cross-section of FIG. 2A. Theouter or "edge" fibers of the linear-array are twisted at first andsecond twists, 22, 24, between which is a substantially straight,parallel section 26. Straight section 26 need not be perfectly straight,but will generally have considerably less rotational slope or "pitch"than the edge fibers at the adjacent twisted portions.

The individual optic fibers are fused together at least along a portionof the straight section 26. As was more fully explained in co-pendingU.S. patent application Ser. No. 08/670,991, filed Jun. 28, 1996, thefull disclosure of which is hereby incorporated by reference, each ofthe twist portions preferably defines one-half of one turn, so that theentire coupler defines a full twist of 360°. Generally, at least one offibers 10A through 10D have been pre-pulled, that is, the fiber has beenheated and elongated to change the diameter and propagation constant ofthat fiber relative to the other optical fibers of the linear-array. Insome embodiments, two or more of the optical fibers will be pre-pulledso that propagation constants of the fibers vary across thelinear-array, as illustrated in FIG. 2A.

As is described hereinbelow, the goal of pre-pulling the fibers is toprovide varying coupling coefficients at each of the fused joints 28across the linear-array. While pre-pulling of the individual fibers isthe preferred mechanism to provide these differing couplingcoefficients, those skilled in the art will recognize that doping ofselective fibers, or some other propagation varying mechanism, couldalso be used to achieve this same result.

Referring now to FIGS. 3 and 3A, a three-fiber linear-array fiber opticcoupler 30 comprises three optical fibers 10E through 10G, the fibersonce again forming a first twist 22, a second twist 24, and asubstantially straight section therebetween 26. At least one of thethree fibers, 10E through 10G, has been pre-pulled prior to fusing thefibers together along at least a portion of the substantially straightsection.

FIG. 4 helps to illustrate what is meant by the term "linear-array" asused in the present application, and also shows that distortions in thelinear-array will have little effect on the performance of the presentcouplers. In the four fiber linear-array optic coupler cross-section ofFIG. 4, the linear-array geometry has been distorted so that the edgefibers are not directly opposite each other. Additionally, the coupledregion between fibers 10C and 10D is substantially larger than coupledregions between other fibers. Nonetheless, fibers 10A and 10D defineedges of the linear-array, while inner fibers 10B and 10C are coupledonly between two adjacent fibers. In other words, a line can be drawn onthe section, beginning at the core of one edge fiber, which passesthrough the cores of each inner fiber, and which ends at the opposededge fiber, but which does not substantially define an enclosed polygon.Hence, the coupler of FIG. 4 remains a linear-array. It should beunderstood that optic couplers of large numbers of fibers might beformed in part as a linear-array, and in part with a hexagonal or otherbundled geometric structure between the edge fibers, within the scope ofthe present invention.

To understand the advantages of the linear-array optic fiber geometry,and to calculate the effects of pre-pulling selected fibers so as toprovide a particular desired power-splitting coupler output, it ishelpful to analyze the propagation of light through the combined waveguide along the coupled length of a simplified linear-array optic fibercoupler.

Linear-Array 3×3 Couplers of Uniform Fibers

To build up an analytical model of the preferred optic fiber couplerillustrated in FIGS. 2 and 2A, we will start with a simple linear-arrayoptic fiber coupler having 3 uniform optic fibers 10I, 10II and 10III asillustrated in FIG. 5. The couplers of the present invention may provide1×N or N×N coupling. We will first analyze the more constrained (andproblematic) N×N output characteristics of these devices. Applyingelectric field amplitude formulae to our linear-array 3×3 coupler ofidentical fibers gives the following: ##EQU1##

Here, a_(i) (z) (i=1,2,3) are the electric field amplitudes at theoutput side of optical fibers 10I, 10II, and 10III, respectively.Similarly, a_(i) (0)(i=1,2,3) are the electric field amplitudes at theinput side of fibers 10I-III. The loss coefficient of the coupler isrepresented by the factor α, which here accounts for real-world couplerimperfections.

The coupling coefficient between adjacent fibers is k. This couplingcoefficient is assumed to be consistent across the fused joints of thislinear-array. In other words, the coupling coefficient between fiber 10Iand fiber 10II is the same as the coupling coefficient between fiber10II and fibers 10I, and is also the same as the coupling coefficientbetween fibers 10II and 10III, etc. The axial length of the couplingregion is z. j represents the imaginary part of a complex number(j=√-1).

Designating the light intensities from fibers 10I, 10II, and 10III atthe output side of the coupler as P₁ (z), P₂ (z), and P₃ (Z),respectively, and similarly designating the light intensities input intothe input side of the coupler fibers 10I, 10II, and 10III as P₁ (0), P₂(0), and P₃ (0), we first assume that a light signal is input only intothe input end of the inner fiber 10II. Thus, the initial condition is P₂(0)=1 (a₂ (0)=1) and P₁ (0)=P₃ (0)=0, and the output light intensitieswill be: ##EQU2## FIG. 5A is a graph of the normalized light intensitiesalso called the power splitting ratios) for variations in the couplinglength z. If we instead assume the signal is input into the edge fiber10I, the initial condition is P₂ (0)=P₃ (0)=0 and P₁ (0)=1, and theoutput light intensities will be: ##EQU3## FIG. 5B illustrates thevariation in light intensities verses coupled length at the output endsof the three fibers when light is input into an edge fiber. Thus, we canmodel the output characteristics of this uniform 3×3 coupler fairlydirectly.

The theoretical model appears to indicate that light input into certainfibers will never be evenly split at the output (see FIG. 5B). Inreality, variations and imperfections in actual linear-array couplersmay produce light intensities verses length characteristics which do notmatch these models precisely. Thus, gradually increasing the coupledlength z (typically by heating the fibers and carefully pulling apartthe input end and the output end while monitoring the light signal atthe output end of each fiber) may eventually provide the desired evenpower distribution. Hence, real world imperfections may occasionallyallow production of a uniform fiber 3×3 linear-array coupler.Nonetheless, the models indicate that repeatable and reliable productionof such couplers will be problematic.

Linear-Array 4×4 Couplers of Uniform Fibers

Turning now to a slightly more complex case, and numbering individualfibers as shown in FIG. 6, electric field amplitudes of a 4×4linear-array fiber coupler with identical fibers will be: ##EQU4## Wherea_(i) (z)(i=1,2,3,4) are the electric field amplitudes at the outputside of fibers 10i, 10ii, 10iii, and 10iv, respectively, and a_(i)(0)(i=1,2,3,4) are the electric field amplitudes at the correspondinginput sides. Excessive loss of the coupler is not considered, k is againthe coupling coefficient of adjacent fibers, z is again the coupledlength, and the following are constants: ##EQU5## If light is introducedinto edge fiber 10i, the initial condition is P₁ (0)=1 (so that a_(i)(0)=1)) and P₂ (0)=P₃ (0)=P₄ (0)=0 then the output light intensities areas follows: ##EQU6## FIGS. 6A and 6B illustrate these light intensitiesfor varying coupled lengths z. This should be representative of thepower splitting which results when light enters an edge fiber.

If a light signal is introduced into one of the two inner fibers, wehave that the initial condition is P₁ (0)=P₃ (0)=P₄ (0)=0 and P₂ (0)=1,and the output light intensities are: ##EQU7## These output intensitiesare shown in FIG. 6C for varying coupled lengths, and the difficulty inreliably producing such 4×4 couplers with even power splitting can beunderstood with reference to that graph.

Linear-Array N×N Couplers of Uniform Fibers

Turning to the more general situation of an N×N linear-array fiber opticcoupler, using fiber numbering similar to that described above, andagain ignoring excessive loss, electric field amplitudes of thesecouplers with identical fibers will be: ##EQU8## Where a_(i) (z), i=1,2, . . . , n are the electric field amplitudes in fibers 1, 2, 3, . . ., n at the output side, and a_(i) (0), i=1, 2, . . . , n are theelectric field amplitudes in fibers 1, 2, 3, . . . , n at the inputside. A_(im), i, m=1, 2, . . . , n are elements of matrix A, a transfermatrix of electric field amplitudes, and λ_(m), m=1, 2, . . . , n areeigenvalues of a characteristic matrix of the coupled mode equation set.As above, z is the coupling length of the coupler.

K is the coupling coefficient of adjacent fibers, and we again assumethat all such coupling coefficients are equal and are real values. Inother words, K=k₁₂ =k₂₁ =k₂₃ =k₃₂ =. . . =k_(n-1),n =k_(n),n-1. P_(i)(z), i=1, 2, . . . , n are light intensities in fiber 1, 2, . . . , n atthe output of the coupler, and P_(i) (0), i=1, 2, . . . , n: are lightintensities of fiber 1, 2, . . . , n at the input side of the coupler.In general, light intensities of such an N×N fiber couplers at theoutput side will be (i=1, 2, 3, . . . , n):

    P.sub.i (z)=(n+1).sup.2 /4Σ.sub.m,q,s,t=1.sup.n sin(n+1/isπ)sin(n+1/msπ)sin(n+1/itπ)sin(n+1/qtπ)e.sup.(.lambda..sbsp.s.sup.+λ.sbsp.s.spsp.*.sup.)z ·√P.sub.q (0)P.sub.m (0)

Bandwidth of Linear-Array Fiber Couplers

The above analysis assumes that all fibers in the linear-array fibercoupler are identical, and that all coupling coefficients betweenadjacent fibers are equal. These assumptions greatly simplify theformula derivations, but as was indicated regarding even the relativelysimple 3×3 case, some properties of the linear-array fiber couplers needmore sophisticated equations to explain. Those properties includebandwidth effects, equal power splitting between the fibers of 4×4couplers, and many other important characteristics.

In practical terms, it is very difficult to find a coupling length atwhich the four output ports of a 4×4 coupler with identical fibers andidentical coupling coefficients have identical light intensities. Toprovide such couplers, we need to provide some additional mechanism tovary the light propagation characteristics across the linear-array, thatis, to control the lateral light coupling from each fiber to the next.

The coupling coefficient between fused fibers has the form of: ##EQU9##Where K.sub.μv is the coupling coefficient between the μth and νth modeof the transverse electric field in the fibers. ω is the angularfrequency of the light propagation in the fibers. ε₀ is the permittivityof vacuum, and P is a light intensity normalization factor. Theequivalent refractive indexes of the fiber cores before and after thecoupling perturbation are n, and n₀, while E.sub.μt and E.sub.νt are thetransverse electric field amplitudes of the eigenmodes in the fibercores. λ is the wavelength of the light propagating in the fiber.

It can be seen that the integral portion of the above equation has arelatively weak dependence on wavelength, so that the overall wavelengthdependence of the coupling coefficient is approximately proportional tothe inverse of the wavelength. Therefore, we can assume the couplingcoefficient will be of the form K.sub.μv =C/λ, C being a constant.

From inspection of the 3×3 coupler formulae given above, we can see thatwhen √2 Kz is equal to some value, say a, then all three output portswill have equal light intensities. If we denote that ##EQU10## Thisindicates that even when a uniform fiber linear-array 3×3 coupler issuccessfully fabricated, only one wavelength will accurately satisfy theconditions required to have three output ports with identical lightintensities. Hence, this explains why couplers with identical fibershave a narrow bandwidth. This sensitivity to signal wavelength is notlimited to 3×3 linear-array couplers, but is instead generally found incouplers having uniform fibers. FIG. 7A shows the variations ininsertion loss at different wavelengths for a 4×4 linear-array fiberoptic coupler having uniform fibers, while FIG. 7B is a similar graphfor a 4×4 bundled fiber optic coupler having uniform fibers and ageometry similar to that shown in FIG. 1B.

To achieve wideband coupling, it would be helpful to make use of lengthdependent coupling techniques. In other words, if K is a function ofboth λ and z, it is possible that the coupler will provide more widebandcoupling characteristics. One approach to vary the coupling coefficientwith changes in the coupled length is to alternate pre-stretched fiberswith unstretched fibers across the array. The variations of couplingcoefficient with the length should be reliable and predictable, so thatthe combined waveguide can be accurately heated and pulled to providethe desired fiber output characteristics.

As described above, one characteristic of the side-by-side geometry ofthe linear-array couplers of the present invention is that each edgefiber is coupled only to one middle fiber throughout the parallelportion of the coupler, while each inner fiber is coupled directlybetween only two adjacent fibers. As was also described above, thecouplers of the present invention are preferably formed by heating andpulling a substantially parallel coupled portion disposed between twotwists. These features and methods help to provide uniform fiber-fiberfusing laterally across the linear-array, regardless of any minordistortions or deviations in the nominal array geometry (as shown anddescribed with reference to FIG. 4).

Additionally, the structure of the couplers shown in FIGS. 2 and 3 willalso minimize mechanical stress-induced variations in the fiber-fiberjoint when the parallel portion 26 is elongated to provide the desiredpower splitting characteristics. In other words, the mechanicalfiber-fiber fusing characteristics of the present linear-array,twist/parallel/twist couplers will be unusually uniform across thelinear-array, and will also be relatively insensitive to variations incoupled length. Hence, where these couplers are formed with uniformfibers, the coupling coefficients will be fairly independent of thecoupled length. Surprisingly, as these couplers are uniform and reliablein their fusing properties, they are also particularly well adapted totake advantage of a separate mechanism--pre-pulling of selectedfibers--to provide a reliable and repeatable variation of couplingco-efficient when the parallel portion is heated and pulled to vary thecoupling length.

To facilitate reliable and repeatable production of a wideband coupler,it will be helpful to analytically calculate the coupler's powersplitting properties when non-uniform fibers are included.

4×4 or 1×4 Linear-Array Fiber Couplers with Unequal CouplingCoefficients.

The following calculations are based on the coupler shown in FIG. 6, inwhich the coupling coefficients K1, K2, and K3 may vary across thelinear-array. The general coupled-mode equations are: ##EQU11## To solvethe above equations, we need to solve the following eigenvector problem:##EQU12## which leads to ##EQU13## which is the same as: λ⁴ +(K₁ ² +K₂ ²+K₃ ²)λ² +K₁ ² K₃ ² =0.

If we denote C₁ =K₁ ² +K₂ ² +K₃ ², and C₂ =K₁ ² K₃ ², then the solutionof the above equation is: ##EQU14## The solution of the coupled-modeequation will have the following form: ##EQU15## where α₁, α₂, α₃, andα₄ are constants which will be determined by the initial conditions, and##EQU16## We have that: ##EQU17## Giving us the following: ##EQU18##Therefore, we have that: ##EQU19## So that, in the 4×4 light intensitymatrix P, Pij can be expressed as follows: ##EQU20## Assuming light isinput into the input end of the first fiber, and denoting: ##EQU21##then output light intensity is as follows: ##EQU22## From the aboveequations, we can calculate the output light intensities at each of thefibers. Numerically, it has been found that when K₁ =0.108, K₂ =0.1722,K₃ =0.1756, and Z=11.4208, then

    I.sub.1 ≈I.sub.2 ≈I.sub.3 ≈I.sub.4 =25%.

FIG. 8 illustrates these output light intensities as a function of thecoupling length z, showing that this particular arrangement provides asubstantially even power split. It should be understood that theabsolute values of these particular coupling coefficients are not asimportant as the ratio between them, for example, K₁ /K₂ and K₁ /K₃.

The above calculation indicate that for 4×4 linear-array fiber couplerswith unequal coupling coefficients, if a light signal is input at fiber1, the output light intensities I₁₋₄ of fibers 10i-iv can generally beexpressed as follows: ##EQU23##

If we want equal output light intensities, we might set I₁ =I₂, I₂ =I₃,and I₃ =I₄, or the like. However, in trying to solve this set of threeequations, we find that we get a relation between K₁, K₂, K₃ and Z, asthere are four variables here. The relationship can be stated in theform K₁ =f₁ (z), k₂ =f₂ (z), and K₃ =f₃ (z).

Alternatively, if we look at form of the multiplying factors whichappear in front of each sine or cosine function, we find that all ofthese multiplying factors are functions of the form ##EQU24## Hence, wecan derive an expression such as: ##EQU25## are coupling coefficientsbetween fibers 1 and 2, fibers 2 and 3, and fibers 3 and 4,respectively. Basically speaking, this tells us that coupling length isinversely proportional to the coupling coefficient times some factor,this factor being a function of certain ratios between the couplingcoefficients.

N×N Fiber Couplers for Wide-Band Coupling

From the solution of the N×N identical-fiber linear-array coupler givenabove, we can see there are only two constants that will affect thecoupling ratio between any two fibers: k, the coupling constant, and z,the coupling length. Restating this in mathematical terms, for eachparticular coupler in which we have N identical fibers fusedside-by-side along identical fused joints, we have only two degrees offreedom--the coupling coefficient and the coupling length. When we haveN fibers, N being an integer greater than two, and when we want toprovide a specific coupling power ratio for each of these N outputfibers, we don't have enough parameters to control or vary to allow usto reliably fabricate our coupler.

While real-world imperfections may allow us to occasionally achieve afairly even power split among three fibers, it will be very difficult tomanufacture N×N couplers of more than three fibers with specified outputcharacteristics. Moreover, precisely and controllably varying thecoupling constant is generally highly problematic. Thus, to provideoptical fiber couplers with more than three fibers, some otherpropagation control mechanism would be helpful.

If we preheat and pre-pull at least one of the fibers defining a fusedfiber-fiber joint, we will vary the coupling constant across that joint.By selectively varying pulling length and time of the fused fibers, wecan use this effect to provide different coupling constants for each ofthe N-1 fused joints in a linear-array coupler of N fibers. We candesignate these joints as follows:

    K.sub.1,2, K.sub.2,3 . . . K.sub.n-1,n,

and we can control the values of the coupling constants (and thecorresponding ratios therebetween) by controlling pre-pull length andtime.

Varying the individual coupling coefficients across the linear-array,generally by varying the pre-pulling length and time, gives us N degreesof freedom we can control. By selecting pre-pull time and lengthproperly, we can use this mechanism to provide any arbitrary couplingratios we want for our N output fibers.

Applying weak-guided wave theory, we can analyze the propagation betweentwo adjacent fibers of a linear-array in isolation. This simplificationis fairly reasonable for the linear-array geometry: for N×N (or 1×N)linear-array couplers, the coupling performance between each pair ofadjacent fibers will be very similar to the propagation between each ofthe fibers in a 2×2 (or 1×2) coupler. In fact, the coupling equationsfor a fused joint are only affected by the fused fibers, and these aregenerally linear equations, so that one fiber added or removed at adistance from the fused joint will not change the coupling performancerelative to wavelength.

To provide different diameters between the two adjacent fibers, one (orboth) is pre-pulled so that it has a smaller diameter (or the two fibersare pre-pulled by different amounts). This difference in fiber diametersgenerally results in different propagation constants in each fiber. Inturn, this difference in propagation constants generally avoids couplingratios of 100% between one fiber and the other fiber, as the lightsignals will travel at different speeds in the two fibers so that theirphases are not matched.

Building further upon this reasoning, we can show that it's possible toreach some arbitrary coupling ratio between our two fibers for differentwavelengths. Still considering our two different fibers, the couplingratio from first fiber to the second fiber will be: ##EQU26## Where k isthe coupling constant, δ=β_(a) -β_(b) is the difference between twopropagation constants, and z is the coupling length. Returning to ourearlier uniform fiber case, β_(a) =β_(b) (so that δ=0), giving us:

    P.sub.2 /P.sub.1 =sin.sup.2 kz

However, we know that if we consider two different arbitrarywavelengths, wherein the two wavelengths are relatively close, eachwavelength will have a different coupling coefficient k. As bothwavelengths will have the same coupling length z, the coupling ratioswill generally not be equal. However,

If β_(a) ≠β_(b) (so that δ≠0), ##EQU27## are two independent parameterswe can control. By properly selecting the pre-pull (or pre-pull ratios),we can have

    P.sub.2 (λ.sub.2)/P.sub.1 (λ.sub.2)=P.sub.2 (λ.sub.1)/P.sub.1 (λ.sub.1)

for different wavelengths, i.e., λ₁ ≠λ₂.

Mathematically, ##EQU28## then I(λ)=A(λ)sin² β(λ)z!.

Since we can pre-pull at least one of our two adjacent fibers, and sincewe can also fuse these two adjacent fibers while pulling both of themtogether, we can control A(λ) and β(λ) independently. By properlysetting our pre-pull amount we can have

    I(λ.sub.1)=I(λ.sub.2) (for λ.sub.1 ≠λ.sub.2).

If we set β(λ) properly, we can also establish a very long period forthe function I(λ). In other words, for wavelengths

    λ.sub.1 <λ<λ.sub.2 (where λ.sub.2 >λ.sub.1),

we can provide I(λ)≈I(λ₁)=I(λ₂). This means we can provide a trulyeffective wideband coupler: a coupler having, throughout a relativelywide region from λ₁ to λ₂, a nearly unchanging coupling power ratio.

Referring now to FIGS. 9A and 9B, the bandwidth improvement provided bypre-pulling selected fibers of a linear-array is illustrated for anoptical coupler of 3 fibers, similar to that shown in FIG. 3A. FIG. 9Aillustrates the insertion loss characteristics at different bandwidthsfor an optical coupler having three uniform fibers. While the insertionloss (and thus the power ratio) at each of the three output fibers isfairly even at a wavelength of 1550 nm, performance degradessignificantly as the wavelength varies from this nominal value. However,by pre-pulling the inner fiber 10F, the insertion loss characteristicscan be substantially flattened to provide approximately even insertionlosses over a much broader range of signal wavelengths, as shown in FIG.9B. Thus, the above analysis is also applicable to linear-array couplershaving some number of fibers other than four.

For an N×N (or 1×N) coupler, the mathematical expression of the couplingratio for N identical fibers is similar to that give above for twofibers: It is a linear combination of sin (kz) and cos (kz). Similarly,for identical fibers, we don't have enough parameters (or degrees offreedom) to control the output intensities at each of the N fibers, andit is difficult to provide the same coupled power ratio for differentwavelengths. In fact, it is difficult to even provide a desired couplingratio among three fibers for a single wavelength.

On the other hand, with proper pre-pull techniques, we can selectivelyvary the propagation constants of each fiber, and, even moreimportantly, can vary the ratios of the coupling coefficients across alinear-array coupler. This variability provides at least N parameters tocontrol, making it possible to provide even power splitting over a rangeof different wavelengths, or even allowing the coupled power ratio to beselected at specific wavelengths. FIGS. 10A-D illustrate just a few ofthe power splitting characteristics which can result.

In FIG. 10A, selective pre-pulling provides a single window 1×3 or 3×3coupler for use when even power splitting is desired only for one targetwavelength at the output of fibers 10E-G, using the fiber numbering fromFIG. 3A. The coupler of FIG. 10B provides a similar dual window 1×3 or3×3 coupler in which the pre-pulling mechanism is used to provide aneven power split at two target frequencies.

An ultra-wide bandwidth selectively pre-pulled linear-array 1×2 or 2×2coupler can be produced having the structure of FIGS. 3 and 3A, asillustrated in FIG. 10C. In this embodiment, one or more of the fibersare pre-pulled, and the parallel portion of the fused fibers are thenheated and pulled until the power output at the inner fiber is less thanhalf the power output of each of the two edge fibers throughout a broadrange of signal wavelengths, and until the two edge fibers exhibit asubstantially even power split throughout the same range. The range willpreferably extend ±30 nm about a target frequency, typically about thenominally coherent frequency of a semiconductor laser.

Alternatively, the two edge fibers may have a substantially even powersplit, while the inner fiber has a lower signal output power which issufficient to monitor the signal with a sensor mounted near the outputend of the middle fiber. Such a coupler is shown in FIG. 10D. The loweroutput at the inner fiber can be substantially less than the even powersupplied to the edge fibers, ideally being less than half the even powerat the edge fibers so that the signal transmitted by the edge fibers ismore robust than would be provided by an even power split among allthree fibers. Optionally, the low power fiber provides a monitor portwhich allows local sensing of the coupled signal. In either case, thepresence of the third fiber generally provides an additional controlvariable to decrease bandwidth sensitivity over a broader range offrequencies relative to two fiber 1×2 or 2×2 couplers. Those of skill inthe art will recognize that linear-array couplers having 4 or morefibers may also be provided having power split characteristics analogousto those of FIGS. 10A-D.

Advantageously, fabrication of fiber optic couplers having any of thepower output characteristics shown in FIGS. 10A-D can utilize commoninitial steps. Generally, jackets 41 are removed from an intermediateportion of the fibers to be coupled, typically exposing about 30 mm ofthe fiber cladding. One or more of the fibers is pre-pulled to vary itspropagation constant, as described above. A clip 40 engages the fibers,preferably over the remaining jacketed portion, and restrains them inthe side-by-side linear-array configuration.

The edge fibers 10A, 10D are then twisted across at least some of theinner fibers to form the first twist 22. The twisted portion of the edgefibers will generally be unjacketed, and the twist will typically defineone-half of a full rotation, so that the edge fibers switch positions asshown. The inner fibers 10B, 10C will typically (although notnecessarily) remain substantially parallel through the twist. The secondtwist 24 is formed in a similar manner, so that the edge fibers ideallydefine a full rotation about the linear-array through the two twists. Asecond clip 40 holds the jacketed fibers so that the twists are betweenthe clips.

A needle-like tool is used to ensure that each twist is as close aspossible to the adjacent clip, maximizing the length of parallel portion26 therebetween. The clips are affixed to movable stages which moveoutward to pull the fibers axially.

The substantially parallel portion is heated with a torch 44, and thefibers are pulled axially in the direction of arrows 46. The twistsprovide a lateral force which pushes the fibers together, promotingfusing between the adjacent heated fibers. While the fibers are pulled,the light intensity at an output end 48 of each fiber 10 is monitored bya sensor 50. Once the output matches the desired coupler outputcharacteristics, the pulling of the fibers stops. Advantageously, thepulling can stop when the coupler exhibits any of a family ofpredetermined coupler power characteristics, including characteristicssimilar to those shown in FIGS. 10A-D, thereby reducing rejection ratesover known coupler fabrication methods which seek only a single couplertype.

An exemplary clip 40 is illustrated in FIG. 12. The clip comprises ametal body 52 having a groove 54 which fittingly receives the opticfibers to be fused together, so as to restrain the fibers in a singlerow. Ideally, the groove is sized to engage jacketed portions of thefibers, as described above. A simple presser 56 holds the fibers in thegroove, the presser ideally comprising an elastomer such as rubber.

While the above description of the specific embodiments has been givenin some detail, for reasons of clarity and understanding, certainmodifications and alterations will be obvious to those of skill in theart. Therefore, the scope of the present invention is limited solely bythe following claims.

What is claimed is:
 1. A fiber optic coupler comprising at least fouroptic fibers, the optic fibers coupled together along a coupled lengthand having input ends and output ends extending from the coupled length,at least two of the optic fibers comprising inner fibers which arecoupled between two adjacent optic fibers, two of the optic fiberscomprising edge fibers which are coupled directly to only one innerfiber along at least a portion of the coupled length, wherein apropagation constant of a first of the optic fibers is different than apropagation constant a second of the optic fibers along the coupledlength, and wherein output light signals of substantially equal powerare produced at the output ends of the optic fibers when a light signalis introduced at the input end of one of the optic fibers.
 2. A fiberoptic coupler as in claim 1, wherein the inner fibers are coupledbetween only two adjacent fibers along the at least a portion of thecoupled length, each of the fibers being disposed side-by-side in asingle row to define a linear-array.
 3. A fiber optic coupler as inclaim 2, wherein the optic fibers define a plurality of fused jointstherebetween along the at least a portion of the coupled length, whereinthe optical fibers along the at least a portion of the coupled lengthdefine a substantially parallel portion, and wherein the edge fibersfurther define first and second twist portions disposed on opposite endsof the parallel portion, the edge fibers along the twist portions beingwrapped around the inner fibers to promote formation of the fused jointswhen the optic fibers are heated and pulled axially.
 4. A fiber opticcoupler as in claim 3, wherein a first fused joint between the first andsecond optic fibers has a coupling coefficient which varies smoothlywhen the parallel portion is heated and the coupled length is increased.5. A fiber optic coupler as in claim 3, wherein second and third fusedjoints have coupling coefficients which are different than the firstcoupling coefficient.
 6. A fiber optic coupler comprising:a plurality ofoptic fibers, each optic fiber defining an axis, the optic fiberscoupled along a coupled length, a propagation constant of a first of theoptic fibers being different than a propagation constant of a second ofthe optic fibers and than a propagation constant of a third of theoptical fibers along the coupled length; a first twist defined by afirst axial portion of two of the optic fibers, each of the twistedoptic fibers having a pitch at the first twist; a second twist definedby a second axial portion of the twisted optic fibers, each of thetwisted optic fibers at the second twist having a pitch; and asubstantially parallel portion disposed between the first twist and thesecond twist, a pitch of the optical fibers along the parallel portionbeing less than the pitch of the twisted optic fibers at the first andsecond twists, the coupled length extending along at least a portion ofthe parallel portion; wherein the optic fibers are coupled side-by-sidein a single row to define a linear-array along the parallel portion, thetwisted fibers being disposed along opposed edges of the linear-array.7. A fiber optic coupler as in claim 6, wherein each fiber has an inputend extending from the first twist and an output end extending from thesecond twist opposite the input end, and wherein coupled power ratios ofthe second ends of the fibers are substantially equal when a lightsignal enters the first end of the first fiber.
 8. A fiber optic coupleras in claim 7, wherein coupled power ratios at the output ends of thefibers are substantially equal when the light signal enters the inputend of any of the fibers.
 9. A fiber optic coupler as in claim 7,wherein there are four optic fibers, and wherein the output end of eachoptic fiber has a coupled power ratio of approximately when a lightsignal enters the coupler along the input end of a first of the fouroptic fibers.
 10. A fiber optic coupler as in claim 7, wherein theoutput end of each optic fiber has a coupled power ratio ofapproximately 0.25 when a light signal enters the coupler along theinput end of any of the four optic fibers.
 11. A fiber optic coupler asin claim 6, wherein each of the optic fibers comprises a cladding and acore, and wherein one of the optic fibers has a coupled power ratio atthe output end which is substantially lower than the coupled powerratios of the other optic fibers.
 12. A fiber optic coupler as in claim11, wherein a signal sensor is coupled to the output end of the lowpower fiber to monitor the coupled light signal.
 13. A fiber opticcoupler as in claim 11, wherein the low power fiber has a coupled powerratio less than half of the other power ratios, and wherein the otherpower ratios remain substantially even over a wide range of light signalfrequencies.
 14. A fiber optic coupler as in claim 6, further comprisingN optic fibers having input and output ends extending from the coupledlength, N being four or more, the output end of each optic fiber havinga coupled power ratio of approximately 1/N when a light signal entersthe coupler along the input end of a first of the N optic fibers.
 15. Afiber optic coupler as in claim 14, wherein the output end of each opticfiber has a coupled power intensity of approximately 1/N when a lightsignal enters the coupler along the input end of any of the N opticfibers.
 16. A fiber optic coupler as in claim 6, wherein at least twofibers are disposed between the two fibers which define the first andsecond twists, and wherein the at least two optical fibers aresubstantially parallel throughout the first twist, the parallel portion,and the second twist.
 17. A fiber optic coupler as in claim 6, whereinpropagation constants of each of the optic fibers are different thanpropagation constants of the adjacent optic fibers.
 18. A fiber opticcoupler as in claim 6, wherein the first twist and the second twist eachdefine approximately one half rotation, and wherein the first and secondtwists together define a full rotation.
 19. A fiber optic coupler as inclaim 6, wherein the coupled power ratios at the output end of thefirst, second, and third fibers are even for light signals within atleast one frequency window, and are uneven for light signals havingfrequencies which are outside the frequency window.
 20. A fiber opticcoupler comprising:at least three optic fibers, each optic fibers havinga core, a cladding surrounding the core, an input end, and an outputend, the optic fibers coupled along a coupled length between the inputends and the output ends, a propagation constant of a first of the opticfibers being different than a propagation constant of a second opticfiber adjacent the first optic fiber along the coupled length; whereincoupled power ratios between one of the input ends and the output endsof at least two of the optic fibers are substantially equal over a rangeof light signal frequencies; and wherein a coupled power ratio betweenone of the output ends and the input end is lower than the equal powerratios over the frequency range, whereby the frequency range of lightsignals providing the equal power ratios is enhanced.
 21. A fiber opticcoupler as in claim 20, wherein the optic fibers are coupledside-by-side in a single row along at least a portion of the coupledlength so as to define a linear-array.
 22. A fiber optic coupler as inclaim 20, wherein a signal sensor is coupled to the output end of thelow power fiber to monitor the coupled light signal adjacent thecoupler.
 23. A fiber optic coupler as in claim 20, wherein the coupledpower ratio of the low power fiber is less than half of the equal powerratios of each of the at least two optic fibers throughout the range oflight signal frequencies.
 24. A method for fabricating optic fibercouplers comprising:providing at least three optic fibers, at least oneof the optic fibers having a propagation constant which is differentthan another of the optic fibers; arranging the fibers side-by-side in asingle row so that two edge fibers are disposed along opposed edges ofthe row; fusing the fibers into a linear-array along a coupled length;heating said fibers and pulling the heated fibers axially to increasethe coupled length; and stopping the heating and pulling step when theoptic fibers exhibit predetermined coupled power ratios.
 25. A method asclaimed in claim 24, wherein the predetermined coupled power ratios ofthe stopping step provides any of a plurality of alternative targetcoupling characteristics.
 26. A method as claimed in claim 24, furthercomprising wrapping said edge fibers about the other fibers of the rowat a first twist, and wrapping said edge fibers about the other fibersof the row at a second twist separated from the first twist, wherein atleast a portion of the coupled length is between the first and secondtwists.
 27. A method for fabricating optic fiber couplers, the methodcomprising:providing at least three optic fibers, one of the opticfibers having a propagation constant which is different than apropagation constant of another of the optic fibers; fusing the fibersalong a coupled length between input ends and output ends of each of theoptic fibers; heating said fibers along the coupled length and pullingthe heated fibers axially to increase the coupled length; and stoppingthe heating and pulling step when the optic fibers exhibit any of aplurality of alternative predetermined coupling characteristics betweenany of the input ends and the output ends.
 28. A method as claimed inclaim 27, further comprising arranging the fibers side-by-side in asingle row along at least a portion of the coupled length, wherein twoof the optic fibers comprise edge fibers disposed along opposed edges ofthe row.
 29. A method as claimed in claim 27, wherein one of thepredetermined coupling characteristics comprises substantially equalpower coupling ratios between an input end and at least two of theoutput ends over a range of input light frequencies, and a powercoupling ratio which is less than the equal power coupling ratiosbetween the input end and a low power fiber over the frequency range,each of the equal power fibers and the low power fibers comprising acore and a cladding surrounding the core.